U.S. Sen. Kelly Ayotte of New Hampshire, who will travel to Ukraine today as part of a three-country trip to the Middle East and Asia, said the United States should broaden economic sanctions against Russia in the wake of that country's annexation of Crimea.

"I commend the President for the sanctions he has announced," she said. "But I believe there are additional steps we could take. I think it's important that the President make a strong statement. We could go even further with the sanctions."

Ayotte spent Thursday in Israel, meeting with Prime Minister Benjamin Netanyahu and President Shimon Peres as well as Palestinian authorities, and traveled to Afghanistan on Saturday, meeting with U.S. military officials and Afghan President Hamid Karzai to discuss U.S. involvement in the country after combat forces are withdrawn later this year.

"This trip has so much to it," Ayotte said Saturday in a phone conversation from the U.S. Embassy in Afghanistan. "These are very important hot spots in the world."

Ayotte's visit to Kiev today comes as Russian troops on Saturday stormed a base in Belbek, fired gunshots in the air and threw smoke grenades, wounding one Ukrainian soldier before Ukrainian forces allowed the Russians to enter, according to wire service reports.

Russia reportedly has also amassed as many as 20,000 troops on the border of southeastern Ukraine. Moscow has called the move a training exercise, but U.S. officials have cast doubt on that claim.

Russia officially annexed Crimea on Friday following a referendum adopted by a vote in Crimea to secede from Ukraine. Ukraine had begun withdrawing its troops from the region, essentially ceding control to Russia, before Saturday's incident.

President Barack Obama on Friday announced sanctions against several wealthy Russian investors with close ties to Russian President Vladimir Putin, but has ruled out any military intervention in the crisis. In response, Putin seemed to make jest of the sanctions, according to wire services, and Moscow barred several prominent Americans from entering Russia, including John Boehner, the speaker of the U.S. House of Representatives, Senate Majority Leader Harry Reid and U.S. Sen. John McCain. Ayotte was not among those prohibited from Russia, though her travel plans do not include the country.

Like Obama, Ayotte said she would not want U.S. troops involved in Ukraine, but believes there is room for more U.S. support for the country.

"I do not support, certainly, any American presence there, but we could support their military" by providing equipment and other support, she said.

Ayotte said she believes Obama made a mistake when he adopted the so-called "reset policy" with Russia, in particular his decision to reverse former President George W. Bush's plan to build defense missile sites in Poland and the Czech Republic.

"The reset policy has failed. It's time to turn this around," she said. "Putin has, time and time again, where we have accommodated him, he has pushed back and taken actions against us or our allies."

She said she would support enacting further sanctions directed at Putin himself and Russia's exporting businesses.

Ayotte said she understands that tougher sanctions against Russia, particularly its natural gas and oil exporting operations, could have implications for the Ukrainian and broader European economies, which are dependent on Russian exports for much of their natural gas.

She said she supports efforts on Capitol Hill to speed up the permitting process for U.S. natural gas exports. The Senate is expected to begin debate on several permitting bills, including one co-sponsored by Democratic U.S. Sen. Mark Warner of Virginia and Republican U.S. Sen. John Hoeven that would require the Department of Energy to approve a permit application within 60 days or provide specific reasons why a permit could not be approved.

While faster permits may not have an immediate effect, "it would send a signal to the markets that we have a long-term solution," she said. "We need to make a strong statement on our energy policy."

In Israel, she said, much of her discussion with Netanyahu and Peres involved ongoing negotiations with Iran over that country's nuclear program.

"I believe we need to maintain sanctions against (Iran) until they finish their work to disarm,'' she said.

In Afghanistan, she said, she had a frank discussion with Karzai about his declining to sign a bilateral security agreement that would provide U.S. troops immunity from local prosecution. Obama has not announced any potential plans for U.S. involvement in post-war Afghanistan without that signed agreement.

"We were very direct with him," she said. "We could not support any more troops being there unless he signed the bilateral agreement."

However, she said she believed that Obama could at least announce a contingency plan should the agreement be signed.

"I think the President needs to make a decision," she said. "A lot of uncertainty could be resolved."

She said she also received an update on the implementation of a law she authored - the No Contracting With the Enemy Act - which was aimed at preventing U.S. Defense contracts from going to companies with ties to U.S. enemies or to companies suspected of corruption. She said she learned that "we've already saved millions of dollars" and that military leaders want Congress to pass pending legislation that extends the rules to the Department of Homeland Security and the U.S. Agency for International Development.

She said she took the trip to hear firsthand the needs in the three countries.

"Being here on the ground is incredibly valuable," she said. "It's one thing to hear someone tell you in Washington, but it's another thing to go into combat theater to see what is on the ground to inform your decision making."

During her time in Afghanistan, which was her third visit to the country since taking office in 2010, Ayotte met with three service members from New Hampshire: Lt. Col. Daniel Stone, Staff Sgt. David Webb and Capt. Nathan Purswell.